How to turn off symmetry in texture paint mode
This option is only available in the upcoming version, 2.75. It's not present in Blender 2.74 so there is no way to enable or disable it in this version.

You can either wait for the 2.75 release or if you want this option right now, download a release candidate version of Blender:

http://download.blender.org/release/Blender2.75/